Let ( = {(1, (2,...} and let A be a -field of subsets of (. Then show

Question:

Let ( = {(1, (2,...} and let A be a σ-field of subsets of (. Then show that
(i) A = P(() if and only if {(i} ( A for all (i.
(ii) A measure μ on A(=P (()) is determined by defining μ ({(i}), i ( 1.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

An Introduction to Measure Theoretic Probability

ISBN: 978-0128000427

2nd edition

Authors: George G. Roussas

See More Books

Question Posted: Mar 25, 2016 03:21 AM

See More Questions

Let V Î¸ be open in R2. A function F: V R2 is said to be conservative on V if and only if there is a function f : V R such that F = f on V. Let (x, y) V and let F = (P, Q) : V R2 be...
Let (1, (2 be two spaces and let A, Ai ( (1, B, Bi ( (2, i = 1, 2. Then show that. (i) (A1 B1) (A2 B2) = [(A1 ( A2] (B1 - B2) + [(A1 - A2)] B1]. (ii) A B = (, if and if at least one of A, B is...
Let A1,..... An be arbitrary subsets of an abstract set (, and let A'i be either Ai or Aci, i = 1,.... n. Define the class C of subsets of ( as follows: C = {all unions of the intersections A'1 (...(...
Will restricting imports affect exports and export-related jobs? How?
Which of the following accounts does not appear in the acquisition and expenditure cycle? a. Cash. b. Purchases returns. c. Sales returns. d. Prepaid insurance.
Calculate without using a calculator. log 8 2 + log 4 2
Define the difference between process and function and provide an example.
Ross Corporation is a debtor in a reorganization proceeding under Chapter 11 of the Bankruptcy Code. By fair and proper valuation, its assets are worth $100,000. The indebtedness of the corporation...
Using a discount rate of 4.5% compounded annually, a pension fund estimates that the present value of its assets and liabilities are $14 million and $13 million, respectively. The duration of the...
1. Why may supplying extra liquidity to banks not necessarily be successful in averting a slowdown in borrowing and spending? 2. Why is there a potential moral hazard in supporting failing banks? How...
Consider the probability space (W, A, P ), where W = {w 1 , w 2 , w 3 , w 4 }, A is the discrete -field, and P is defined by For n = 1, 2,, define A n by: A 2n1 = {w 1 , w 2s }, A2n = {w 1 , w 2 }....
Suppose that ( = {(1, (2,...}, and let A be the discrete Ï-field. On A, define the set function Î¼ by Then show that (i) Î¼ is nonnegative, Î¼(Ã = 0...
In a recent year, 73% of first-year college students responding to a national survey identified being very well-off financially as an important personal goal. A state university finds that 132 of an...
Direct costing produces income statements that are a more accurate reflection of the true profit fluctuations than the income statements produced by absorption costing. State briefly why you either...
Define break-even analysis and outline its uses and applications.
A break-even chart must be used with intelligent discrimination, with an adequate grasp of assumptions underlying the technique surrounding its practical application. Elucidate the statement giving...
Explain briefly the non-financial measures of quality and customer satisfaction.
The effect of a price increase is always to increase the P/V ratio, to bring down the break-even point and to widen the margin of safety. Discuss.
Darren, I know you are trying hard, but its not about effort; I give merit raises based on results. Identify the factor contributing to low performance in the following five situations. A. Ability B....
An annual report of The Campbell Soup Company reported on its income statement $2.4 million as equity in earnings of affiliates. Journalize the entry that Campbell would have made to record this...
Each of three machined parts is classified as either above or below the target specification for the part.
Each of four transmitted bits is classified as either in error or not in error.
In the final inspection of electronic power supplies, three types of nonconformities might occur: functional, minor, or cosmetic. Power supplies that are defective are further classified as to type...
You have just made your first $5,200 contribution to your retirement account. Assume you earn a return of 12 percent per year and make no additional contributions. a. What will your account be worth...
There are two components of leadership. The first is your own personal style and the second is how you choose to lead. Use the following checklist to evaluate your leadership style: What Kind of a...
Selected Realized Returns, 1926-2017 Average Return Standard Deviation Small-cap stocks 16.5% 31.7% Large-cap stocks 12.1 19.8 Long-term corporate bonds 6.4 8.3 Long-term government bonds 6.0 9.9...

Let ( = {(1, (2,...} and let A be a -field of subsets of (. Then show

Question:

Step by Step Answer:

i If i A for all i then clearly every s...View the full answer

An Introduction to Measure Theoretic Probability

Students also viewed these Statistics questions